Editor's Note: Matthew Lane is a Ph.D. candidate in mathematics at UCLA, and is the founder of Math Goes Pop!, a blog focused on the surprisingly rich intersection between mathematics and popular culture. He is also a contributor to the Center for Election Science. You can follow him on Twitter at @mmmaaatttttt.

When the Avengers assemble, the world opens its collective wallet. In just under three weeks since its international opening, "Marvel's The Avengers" has earned more than $1 billion worldwide. In America, it blew through the $200 million mark over opening weekend alone, and now holds the title of best three-day opening in film history. Or does it?

While dollar signs fuel the engine of Hollywood movie production, they are not necessarily the most objective measure of a film's success. Most importantly, the dollar is not a static unit of measurement like the meter; as a result of inflation, a dollar in 2008 has more purchasing power than a dollar in 2012. If we search for a better way to measure film's opening weekend success, is it possible to dethrone the mighty Avengers? Let's try to find out.

If we look only at unadjusted gross opening weekend revenue, the top 10 most successful films of all time are as follows, with the amount of money earned in parentheses:

"Marvel’s The Avengers" ($207,438,708)

"Harry Potter and the Deathly Hallows: Part 2" ($169,189,427)

"The Dark Knight" ($158,411,483)

"The Hunger Games" ($152,535,747)

"Spider-Man 3" ($151,116,516)

"The Twilight Saga: New Moon" ($142,839,137)

"The Twilight Saga: Breaking Dawn, Part 1" ($138,122,261)

"Pirates of theCaribbean: Dead Man’s Chest" ($135,634,554)

"Iron Man 2" ($128,122,480)

"Harry Potter and the Deathly Hallows: Part 1" ($125,017,372)

This data, and all data that follows, has been pulled from Box Office Mojo. Notice that Hollywood’s love affair with the sequel can be explained in large part by this list: of these films, only one, "The Hunger Games," is not a sequel, and even this one is not a new property, but is based on the hugely successful book by the same name.

By this measure, "The Avengers" is the clear front-runner. However, it is one of only two films on this list to have been released in 2012. If we adjust these opening-weekend figures to account for inflation, how much does the picture change?

Thankfully, Box Office Mojo has already performed the necessary calculations. They do this by adjusting a film’s revenue to take into account the average ticket price in the year it was released. For example, "The Dark Knight" made roughly $158 million in 2008, when average ticket prices were $7.18. In 2012, the average has increased to $7.92 (see here for a complete list of yearly averages). This means that if we want a more accurate comparison of this film to The Avengers, we should multiply its opening weekend gross by the ratio of the 2012 average price to the 2008 average price. This ratio is $7.92/$7.18 or approximately 1.10, meaning that The Dark Knight’s opening gross in 2012 dollars would be closer to $175 million.

By this measure, the top 10 films are as follows (now the amounts are adjusted to 2012 dollars):

"Marvel’s The Avengers" ($207,438,708)

"The Dark Knight" ($174,738,000)

"Spider-Man 3" ($173,959,700)

"Harry Potter and the Deathly Hallows: Part 2" ($168,763,300)

"Pirates of the Caribbean: Dead Man’s Chest" ($164,003,900)

"Spider-Man" ($156,551,700)

"The Hunger Games" ($152,535,747)

"The Twilight Saga: New Moon" ($148,657,800)

"Shrek the Third" ($140,015,100)

"The Twilight Saga: Breaking Dawn, Part 1" ($139,709,900)

Remember, these numbers are estimates, and while they are useful for making more objective comparisons, they should still be taken with a grain of salt. Even so, a quick look at this list shows it varies slightly from the unadjusted one. In both cases, however, "The Avengers" is on top.

These adjusted revenues, however, allow us to create one more measure of a film’s opening-weekend success. Since we know the opening-weekend revenue and the average ticket price, we can compute the estimated number of tickets sold during the weekend. The top 10 list for tickets sold will be the same as adjusted revenue list shown above, since an estimate for the number of tickets sold can be found by dividing the adjusted revenue by $7.92, the average 2012 ticket price.

Let’s combine this with one other piece of information: the number of theaters screening the film opening weekend. If we know how many tickets were sold and how many theaters were playing the film, we can estimate the number of tickets sold per theater to get a sense for how packed the theater was during opening weekend. By this metric, the top 10 list for largest opening weekend in a wide release has quite a few surprises (the number in parentheses are now estimates for number of tickets sold per theater):

"Hannah Montana/Miley Cyrus: Best of Both Worlds Concert Tour" (6,346)

"Marvel’s The Avengers" (6,022)

"Spider-Man" (5,468)

"The Blair Witch Project" (5,222)

"Spider-Man 3" (5,166)

"The Dark Knight" (5,053)

"Pirates of the Caribbean: Dead Man’s Chest" (5,010)

"Harry Potter and the Deathly Hallows: Part 2" (4,871)

"Borat" (4,826)

"The Lost World: Jurassic Park" (4,790)

We have discovered the secret to defeating "The Avengers": Miley Cyrus. While some may be critical of this metric on the grounds that it inflates the averages for films with a relatively small release (the Hannah Montana film opened on only 683 screens, compared to 4,349 for The Avengers), this data still tells us something about the level of anticipation for each of these films. In particular, the Hannah Montana film probably should have opened on a larger number of screens.

Note that this top 10 list only considers films that earned at least an unadjusted $25 million in their opening weekend. So there may be more surprises among a larger family of films.

One could also think of more ways to slice the data. For example, "The Avengers" didn’t have the largest opening day ever, but held its ground very well over the weekend, allowing it to eclipse competitors like "Harry Potter." By digging through the data, one could compare day-by-day performance over opening weekend,and use this metric to rank films. One could also try to account for changes in population size over time.

No matter how you slice it, though, "Marvel’s The Avengers" is doing exceptionally well. But as Miley Cyrus has taught us, there is still room for this superhero team to grow.

soundoff(63 Responses)

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November 23, 2012 at 3:24 am |

Bill Brasky!!!!

Freddy Got Fingered is a cinematic GEM!

May 26, 2012 at 5:52 am |

Cliff

Nothing about this is right. It's muddy math that doesn't work in the real marketplace. One of the reasons Hannah Montana sold so many tickets per screen is BECAUSE it was only in 683 theaters. By Matthew Lane's logic, you could use the same math to realize that "Precious" sold more than TWICE AS MANY tickets opening weekend per theater than HM or Avengers. But it only played on 18 screens. When it opened wider a few weeks later (on 629 screens) it's number of tickets sold per theater (even though it's weekend BO was more than 5x then when on 18 screens) was less than 1/5th the amount when on 18 screens.

Hannah Montana was a hit, no doubt, but MOST of what gave it it's phenomenal per screen average can be attributed to these facts...
A) It's screen count was so low.

B) 96% of HM's screens were 3D (a much higher percentage than Avengers had) and most of those 3D exhibiters were charging a special event $15 per ticket charge instead of the average $7.92 used in Matthew Lane's math (Avengers 3D only did 52% of it's money from 3D and IMAX that weekend).

and C) Disney advertised Hannah Montana as a "1 Week Only Limited Engagement." This was a total lie and the film crashed 69% on weekend 2 when all that upfront demand had been expended. Had The Avengers been advertised as being for 1 week only... hmmm.

So to summarize... Matthew Lane clearly didn't do a lot of research before writing this. He's comparing apples and turkeys. What actually makes Avengers more successful AND impressive is that it did that per screen average WITH that high screen count. Stories of every singe IMAX seat being sold that weekend are impressive. If you have 500 seats and you sell them out, OK, but big deal. If you have 500,000 and do the same... impressive.

May 21, 2012 at 2:44 am |

Rob

They should go by ticket sales, if they do that the top movies of all time would probably still be the likes of Jaws, Star Wars, etc... Movies that cost like $2 to see, and played before the golden age of VHS.

May 20, 2012 at 10:52 am |

Steven Morrow

Economists and financiers have already done that (On a side note, this article has horribly incorrect mathematical formulation, but...). By ticket sales alone, Gone with the Wind would still be the most widely viewed film in theaters, a proven fact. However, an argument could be made that at that time there was no television or multiplexes. When one film came out, that was it. It would be shown with another film (the extinct Double-Feature that was commonplace back then). As far as Jaws and Star Wars, again, there was no cable, no VHS or DVDs, and the multiplex was at its most nascent stages. More choices dilutes the ticket-purchase power any single film can wield today. Also, they track the money more than ticket sales because that's all studios care about... money.

June 6, 2012 at 6:59 pm |

OH MY JEBUS

FINALLY! Someone gets that Hannah Montana was the best movie ever.

Thanks Math.

May 20, 2012 at 10:15 am |

CBC

LOL! Thanks for the additional laugh!

May 20, 2012 at 11:10 am |

Sriram

Best movies are..... Sound of Music, Ben-Hur, Ten Commandments, Gone with the Wind, Casablanca, Good,Bad and the Ugly.... What great movies!

With no computers and graphics.....the chariot race, the parting of the Red sea......WOW!!!!

May 20, 2012 at 9:50 am |

Tim

See, math can be fun, and not taken to seriously.

May 20, 2012 at 9:30 am |

Tim

I'm pretty sure that if The Avengers had a limited release it would have filled theaters more than the Hannah Montana movie.

May 20, 2012 at 8:36 am |

ken845

I haven't gone to see any of these movies.

May 20, 2012 at 8:21 am |

4th wright

I guess the best team in baseball must be the Chicago Cubs then?

May 20, 2012 at 8:05 am |

asdf

EXACTLY. Well, if we only count doubles hit and divide that by earned runs for only starting pitchers....

May 20, 2012 at 9:42 am |

alpgr49

The latest in the "Planet of the Special Effects" series. No insight into the human condition. Computer-generated eyewash.

May 20, 2012 at 7:40 am |

LOL!

Only a nerdy mathematics major would believe box office sales indicate how great a movie is.

May 20, 2012 at 4:50 am |

Aardie

I want to see the list based on total number of tickets sold.

May 20, 2012 at 1:49 am |

kdub74

Check out the description of the second list. It takes into account inflation based upon the average cost per ticket in a given year. That list is essentially the same as a "per ticket sold" list.

May 20, 2012 at 5:52 am |

MandoZink

kdub74 – At first I thought you were wrong, but you are correct. The second list would be exactly proportional to tickets sold.

May 24, 2012 at 12:01 pm |

Liebster Welpe

Best movie 2012: John Carter

May 20, 2012 at 12:58 am |

David, Columbus

If you take into account inflation, the number 1 grossing movie of all time is "Gone With the Wind", and number 2 is one of the Star Wars sequels, I believe. The method used here does not adjust ticket prices back far enough in the past, and the methods used by the movie industry to rank movies are a joke.

May 19, 2012 at 11:02 pm |

Victor Schwartzman

Agree re Gone With the Wind. However, these measures are purely commercial. Is not the most important measure how many people have seen the film–how many tickets have been sold? You'll note that all the films Matthew lists are recent. That's not because more people necessarily saw them, but because of ticket prices. With respect a much better and more interesting article would look at number of tickets sold. But of course, that would list much older films, and not new films which enjoy this type of commercial approach.

May 19, 2012 at 11:48 pm |

JoeyATL

Absolutely. Gone With The Wind sold way more tickets than any of Hollywoods later blockbusters. And you have to remember that there was no TV when it came out. It played in theaters forever. And even played on the big screen in the CNN center in Atlanta everyday up until a few years ago. It's the biggest movie of all time.

May 20, 2012 at 2:45 am |

Flanny

I agree. Statistics give so much room to have 'fun' with studies. This article cleared up nothing. Boo reporting.

May 20, 2012 at 3:03 am |

kdub74

Actually the method that they use (boxofficemojo) does in fact go back that far, it takes into account ticket prices all the way back to the early 30's (possibly even earlier) Gone with the wind is the all time domestic champ overall, but what is listed above is opening weekend, and GWtW didn't even come close to sellign the number of tickets that the movies on this list did. However it had tremendous staying power and stayed popular for a long long time as well as all of it's re-releases. Thats why it is #1 currently.

May 20, 2012 at 5:56 am |

Edward

Neither Gone With the Wind nor the first two Star Wars movies opened in a saturated, national release. And in the case of GWTW, one cannot use the traditional gross divided by average ticket price modifier, since GWTW was a roadshow presentation its first few years at ticket prices up to 12X the normal area ticket price, depending on where one saw it.

May 21, 2012 at 10:12 am |

Keats

Don't forget that movies such as "Star Wars" have re-releases that add to their totals. I don't see why you couldn't evaluate a movie by the number of tickets sold. Saturated markets isn't a valid argument. People still had to buy tickets to see the shows. They're not plane flights.

As a Buckeye fan I would have to agree. Worst. Year. Ever!!! I? just don't see how you can have a highlight film with the worst QB to ever play at Ohio State and prblaboy the worst QB in all of college football.This team was a train wreck.

June 28, 2012 at 8:49 am |

Chad

Going back to the math...

There is one important point which is important to note, which is the per capita distribution of movie theaters. While perhaps not very significantly different between 2010 and 2012, there is surely some difference between even just a decade, let alone multiple decades.

Inflation is an important metric, but we must also consider the TOTAL population, vs. the TOTAL number of movie theaters. It is quite possible that while America's population may have been only half of what it is now 50 years ago, there MAY have been a higher theater / person ratio (though unlikely).

Thoughts?

May 19, 2012 at 9:59 pm |

CS

The only way to judge a movie’s “greatness” is to gage longevity...how popular a movie is over at least five years, combined with both amateur and professional critical assessments of acting, script and cinematography.

Money is stupid measure of "how good" a movie is. Too many random factors play into when people can see movies and ticket prices fluctuate too much. Inflation is not easy to adjust for either.

Even counting viewers is flawed, because the earth's population has increased dramatically since movies were invented and people’s habits and median age change. Maybe how many people per capita saw a movie would work better, but that is flawed too.

The only way is to gage longivity...how popular a movie is over time, combined with both amature and professional critical assessments.

May 19, 2012 at 8:56 pm |

Scott

Avengers is one of the worst movies I've seen in a long time, and I'm absolutely appalled Americans are seeing it in droves, or in the case of many people I know, seeing it MULTIPLE times! In a nutshell it proves how dumb people are becoming and that they can be entertained by anything as long as it has explosions, aliens, and lasers. This is a movie for 5 year old boys.... not a bunch of adults. Can you say CHEESE!?

May 19, 2012 at 8:17 pm |

JD

Obvious troll is obvious

May 19, 2012 at 9:12 pm |

Dylan

Some people like superhero movies, you know...

May 23, 2012 at 7:55 pm |

Dave

And some people don't. Just because he doesn't like it doesn't mean he is a troll. I thought the avengers was okay...it had great action scenes, but that's about it.

June 4, 2012 at 1:21 pm |

Money doesn't matter

They shoud just count the total number of tickets sold throughout the run of the movie. Tickets are wwwaaaaaaaay overpriced, so some people may wait until the end of the run when it goes into the cheaper theaters. Only flaw there is that some people may see the movie more than once, but it's way better than calculating the $total$ revenue, which will always increase. And I can't remember the last time I spent less than $9 for a movie ticket, so using the average price to calculate a ticket, over the millions of tickets sold, isn't quite that accurate. Tickets can be counted, so count them!!!!

May 19, 2012 at 7:57 pm |

kdub74

reread what was written about the second list. It's inflation adjusted by the average ticket cost, so it is essentially arranged by how many tickets were sold.

May 20, 2012 at 6:02 am |

Bob Roitblat

When you adjust for inflation, Gone with the Wind sold way more tickets–about 7 times more–to a population half the size. Star Wars sold more tickets, as did E.T.

May 19, 2012 at 7:37 pm |

Mark Knight

The type of theater opening it had will also increase the box office intake as well. When Harry Potter and the Deathly Hallows Part 2 was released it was only shown at the theater I saw it on with, 1 3D screen, 1 XD digital screen and 3 regular screens. Now the 3D and XD (Xtreme Digital) screen charged like $4.00 more per ticket over the regular screen amount. When The Avengers came to the same theater, it was shown on 3, 3D screen, 1, XD screen and 1 regular screens.

Now you do the math...

May 19, 2012 at 7:23 pm |

Independent from NH

Exactly. Well said.

May 20, 2012 at 12:45 am |

Jesparza

I say the most successful movies are the ones that sell the most tickets. Plain and simple. If back in the "30's Gone With The Wind sold more tickets than The Avengers did now, it shouldn't matter that the tickets back then only cost $.05 cents. If you only look at money, there will always be a more successful movie, no matter how badly the movie sold.

May 19, 2012 at 6:39 pm |

bruce

to me, the best films are based not on box office, but the combination of script, cinematography & acting. on that basis, the best ever is The Lion in Winter. hands down.

May 19, 2012 at 6:26 pm |

John

"Duh" to the first part of your comment and "Huh?" to the second.

May 19, 2012 at 10:39 pm |

tested

Even though the author is a Math PhD I believe the statement "We have discovered the secret to defeating "The Avengers": Miley Cyrus." and "In particular, the Hannah Montana film probably should have opened on a larger number of screens." is flawed. Since the Hannah Montana film opened on only 683 screens, compared to 4,349 for The Avengers assuming that the per theater tickets will remain the same in both instances is incorrect. By virtue of only opening in a smaller number of theaters the movie is likely to get a higher number of per theater tickets (than a movie opening in a larger number of theaters). Further assuming that opening in more theaters would not have decreased the per theater number of tickets is an unfounded assumption.

Given that it is possible to mathematically test if the presented statement is true by including the number of theaters as an explanatory variable in a simple analysis this simple numeric manipulation that is presented is insulting to the reader and mathematicians in general.

Yes it is true that you can slice the data in many ways and try to show different results, but isn't it a scientists (or mathematician in this case) responsibility to use proper methods to accurately analyze the data (instead of searching for a biased method that presents the results that you want).

May 19, 2012 at 6:21 pm |

kdub74

I believe (hope) that his comment was tongue in cheek and merely served the dual purpose of providing a chuckle and showing that theres many different ways you can look at the statistics to end up with some odd results.

May 20, 2012 at 6:00 am |

Howard

I don't understand why a movie's success is based on money rather than tickets sold.

May 19, 2012 at 5:53 pm |

Hadenuffyet

you can't spend a ticket...

May 19, 2012 at 6:00 pm |

John

Ridiculous response, of course. A movie's popularity should be based on the number of tickets sold. It's the only unit of measurement that doesn't change with inflation or the even the simple cost of the ticket.

May 19, 2012 at 10:38 pm |

devils advocate

What would be interesting is what % of the population saw a movie (ticket sales/population) I wonder how some older movies would do using this metric.

May 19, 2012 at 4:55 pm |

Stinky

Why are you only looking at opening weekend numbers? It seems to me that would only measure the level of hype of a movie, not how "successful" it was.

May 19, 2012 at 3:49 pm |

Victor Matheson

Since the Avengers has only been in the theater for a couple of weeks, the author doesn't have the full box office data. In order to do an apples to apple comparison, he can only use opening weekend data at this point.

May 20, 2012 at 8:02 am |

davetharave

They will never make a better movie than Casablanca, no matter what they try. This movie has a great cast, powerful story with romance, wartime intrigue, nazis (hate those guys) and a reluctant hero who shows his true colors at the end. How will they ever top Casablanca ?

May 19, 2012 at 3:49 pm |

Hadenuffyet

my question is ,how did Borat get on any of the lists , I'd rather watch paint dry..

May 19, 2012 at 6:02 pm |

CS

I agree with Ingrid Bergman's assessment of Casablanca. There are a lot of better movies. Lawrence of Arabia, African Queen, Bridge on the River Kwai are some of the better old movies. Godfather, Shawshank Redemption, Seabiscuit, LA Confidential, When Harry Met Sally, Gandhi, Sideways, Rain Man, and Master and Commander are better modern movies.

May 19, 2012 at 8:46 pm |

Mmmyesss

Borat was hilarious lol.. Tho I am surprised that it got on the list

May 20, 2012 at 10:29 am |

Lewis

What is amazing about this film is not only are the Box Office numbers outrageous, but the reviews from both critics and audiences are overwhelmingly positive. This is a blockbuster that lives up to the hype and deserves every penny it's made.

May 19, 2012 at 3:47 pm |

Keats

This is stupid. Adjust for all movies and the winner is still "Gone with the Wind." The fact is tickets go up in price and everyone charges an increased premium for 3-D. Add in, as I recall, since the early 1990's, theaters/studios always open big movies on multiple screens.

May 19, 2012 at 3:47 pm |

Ryan in Texas

Also, there were less people in the US in the past.
A real metric would be percent of all tickets sold. That way it would account for less people, less movie goers – and it completely takes inflation out of the issue. So we would really see the dominance of Star Wars or Gone with the Wind, if those are still top level draws by this better metric.

May 19, 2012 at 3:42 pm |

J

I've always wondered why records are established by dollar amounts. Surely, tickets can be counted, right? Then average ticket price does not even have to be calculated. Just count how many tickets were sold!

May 19, 2012 at 3:08 pm |

Cls

While an interesting way of looking at things, one line stands out:
"In particular, the Hannah Montana film probably should have opened on a larger number of screens"
I think part of the reason for the films high ticket/theater ratio is that is was limited in the number of theaters it was played at. so those who wanted to see it had limited places to go, therefore, packing the theater every time.
By this logic, every time i watch a movie in my living room, its a sold out show. Proving even a lowly citizen as myself, is mightier than the avengers.

Math: it can always be manipulated to show us exactly what we want to see.

May 19, 2012 at 3:06 pm |

Derrick, Atlanta

If they are measuring how great or significant a movie is, maybe they should also look at a "before-and -after" ratio of the movie's ratings instead of just the volume of interest in the movie. Some movies are overhyped and some movies are underhyped.

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